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# Communications in Number Theory and Physics

## Volume 10 (2016)

### Number 3

### Monstrous BPS-algebras and the superstring origin of moonshine

Pages: 433 – 526

DOI: http://dx.doi.org/10.4310/CNTP.2016.v10.n3.a2

#### Authors

#### Abstract

We provide a physics derivation of Monstrous moonshine. We show that the McKay–Thompson series $T_g, g \in \mathbb{M}$, can be interpreted as supersymmetric indices counting spacetime BPS-states in certain heterotic string models. The invariance groups of these series arise naturally as spacetime T-duality groups and their genus zero property descends from the behaviour of these heterotic models in suitable decompactification limits. We also show that the space of BPS-states forms a module for the Monstrous Lie algebras $\mathfrak{m}_g$, constructed by Borcherds and Carnahan. We argue that $\mathfrak{m}_g$ arise in the heterotic models as algebras of spontaneously broken gauge symmetries, whose generators are in exact correspondence with BPS-states. This gives mg an interpretation as a kind of BPS-algebra.